Note: At the moment (08/19/205) the player is generating a script error when you select the trailer videos (in the other videos is normal), the error is as follows:
Uncaught Referenceerror: Numberutility is not defined - share2_combined.min.js? 34123595:1
At the time of selecting the video in embed you should click on + Show options, as in the image:

This will appear, in it select the autoplay:

The code should look like this:
<iframe src="https://player.vimeo.com/video/75187319?autoplay=1&title=0&byline=0&portrait=0" width="500" height="281" frameborder="0" webkitallowfullscreen mozallowfullscreen allowfullscreen></iframe>
And the URL should look like this https://player.vimeo.com/video/75187319?autoplay=1&title=0&byline=0&portrait=0
Note: I recommend using html & instead of &, although Html5 normally accepts the & without the amp; you may still have a number of eventual problems, for example if you hear an SVG on your page or something relating to XML.
Note that if autoplay is not occurring it may be a matter of sandbox in your lightbox that uses iframes.
To complement the answer of @balexander, you must use the class fancybox.iframe within the attribute class="", should look like this:
<!DOCTYPE html>
<html>
<head>
    <title>Exemplo</title>
    <!-- Adiciona biblioteca jQuery -->
    <script type="text/javascript" src="http://code.jquery.com/jquery-latest.min.js"></script>
    <!-- Adiciona FancyBox -->
    <link rel="stylesheet" href="/fancybox/source/jquery.fancybox.css?v=2.1.5" type="text/css" media="screen" />
    <script type="text/javascript" src="/fancybox/source/jquery.fancybox.pack.js?v=2.1.5"></script>
    <script>
    $(document).ready(function() {
        $(".fancybox-media").fancybox({
            maxWidth    : 800,
            maxHeight   : 600,
            fitToView   : false,
            width       : '70%',
            height      : '70%',
            autoSize    : false,
            closeClick  : false,
            openEffect  : 'none',
            closeEffect : 'none'
        });
    });
    </script>
</head>
<body>
    <a class="fancybox-media fancybox.iframe" href="https://player.vimeo.com/video/75187319?autoplay=1&title=0&byline=0&portrait=0">Play</a>
</body>
</html>
Using Nivo-Lightbox:
It should look like this (requires version 1.2.0), download the files from https://github.com/gilbitron/nivo-lightbox
<!DOCTYPE html>
<html>
<head>
    <title></title>
    <link rel="stylesheet" href="nivo-lightbox.css" type="text/css" />
    <link rel="stylesheet" href="themes/default/default.css" type="text/css" />
    <script src="https://ajax.googleapis.com/ajax/libs/jquery/1.10.1/jquery.min.js"></script>
    <script src="nivo-lightbox.min.js"></script>
    <script>
    $(document).ready(function(){
        $('a').nivoLightbox();
    });
    </script>
</head>
<body>
    <a href="https://player.vimeo.com/video/75187319?autoplay=1&title=0&byline=0&portrait=0" data-lightbox-type="iframe">Carregar video</a>
</body>
</html>
							
							
						 
try to see this topic: https://vimeo.com/forums/topic:1506
– balexandre